NEED-BASED FEEDBACK: AN OPTIMIZATION APPROACH By DEBRAJ CHAKRABORTY A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy NEED BASED FEEDBACK: AN OPTIMIZATION APPROACH By Debraj Chakraborty August 2007 Chair: Jacob Hammer Major: Electrical and Computer Engineering Feedback is often used to overcome the adverse effects of perturbations and uncertainties on the performance of engineering systems. However, failures of the feedback channel cannot be completely avoided. This dissertation addresses the questions of how and for how long can desirable performance of a perturbed system be maintained after a failure of the feedback channel. Let Σε be a system that is subject to a perturbation ε in its parameters. The exact value of the perturbation ε is not known; it is only known that ε is bounded by a given constant δ. Now, let u(t) be an input function of Σ, and let Σεu be the response of the perturbed system to the signal u(t). The nominal system is Σ0, and the nominal response to the signal u is Σ0u. Therefore, the deviation in the response caused by the perturbation is ||Σεu – Σ0u||. To reduce the perturbation, add a "correction signal" v(t) to the input signal, so that the perturbed response becomes Σε(u+v). Then, the new deviation between the perturbed and nominal cases becomes ||Σε(u+v) – Σ0u||. The correction signal v(t) must be independent of perturbation value ε, as the latter is not known. Let M be the maximal deviation allowed for the response, and let tf be the time for which ||Σε(u+v) – Σ0u|| ≤ M. Then, the objective is to find a correction signal v(t) that